Smart obstacles in time dependent electromagnetic scattering

Smart (or active) obstacles are obstacles that, when illuminated by an incoming field, react by actuating a policy in order to pursue an assigned goal. The design of smart objects can be improved by the availability of satisfactory mathematical models. We propose the use of models based on optimal control problems to describe the behaviour of smart objects. We restrict our attention to the context of time dependent electromagnetic scattering. In this context, the smart obstacle, in order to pursue its goal, circulates on its boundary a surface electric current density. The optimal control problems associated with these obstacles give a way of characterizing and computing the current densities needed as optimal solutions of the mathematical problems considered. The goal pursued by smart obstacles is one of the following: 1) to be undetectable (i.e. furtivity problem); 2) to appear to have a different shape (i.e. masking problem); 3) to appear in a different location from its actual one (i.e. ghost obstacle problem). We concentrate on furtivity and masking problems in time dependent three dimensional electromagnetic obstacle scattering.